Kantor Triple Systems
Research output: Thesis › Doctoral Thesis (compilation)
Abstract
The main purpose of this thesis is to study real exceptional Kantor triple systems. In the first paper we first prove the known results in both the real and complex classical cases of Ksimple Kantor triple systems. In the real classical case our approach gives somewhat simpler formulas. Special attention is given to all real classical cases of Ksimple Kantor triple systems that can be presented in another isomorphic form, i.e. defined on tensor products of composition algebras. They are of interest in their own right and help to understand the real exceptional case. Then we consider the real exceptional Ksimple Kantor triple systems. The main result of the first paper is the classification up to weak isomorphism of all real exceptional Ksimple Kantor triple systems defined on tensor products of composition algebras. Also, a description of the split and the five remaining cases is given. In the second paper we develop the main result of the first paper and give a classification up to isomorphism of real simple compact Kantor triple systems defined on tensor products of composition algebras. The classification is given by presenting a unified formula for multiplication in these triples. In addition, we obtain an explicit formula for the canonical trace form for real simple compact Kantor triple systems defined on tensor products of composition algebras.
Details
Authors  

Organisations  
Research areas and keywords  Subject classification (UKÄ) – MANDATORY
Keywords

Original language  English 

Qualification  Doctor 
Awarding Institution  
Award date  2003 Feb 10 
Publisher 

Print ISBNs  9162855131 
Publication status  Published  2002 
Publication category  Research 
Bibliographic note
Defence details
Date: 20030210
Time: 10:15
Place: MH:C
External reviewer(s)
Name: Mazorchuk, Volodymyr
Title: ass. Prof
Affiliation: Uppsala Univ., Uppsala, SWEDEN
